Scholarlink

<p>We calculate the Seiberg–Witten invariants of branched covers of prime degree, where the branch locus consists of embedded spheres. Aside from the formula itself, our calculations give rise to some new constraints on configurations of embedded spheres in 4-manifolds. Using similar methods, we also obtain new constraints on embeddings of real projective planes and spheres with a cusp singularity. Moreover, we show that the existence of certain configurations of surfaces would give rise to 4-manifolds of non-simple type. Our proof makes use of equivariant Seiberg–Witten invariants as well as a gluing formula for the relative Seiberg–Witten invariants of 4-manifolds with positive scalar curvature boundary.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Constraints on embedded spheres and real projective planes in 4-manifolds from Seiberg–Witten theory

  • 期刊论文

  • 发表日期：

    2026年5月27日

查看全文
  • David Baraglia

摘要

We calculate the Seiberg–Witten invariants of branched covers of prime degree, where the branch locus consists of embedded spheres. Aside from the formula itself, our calculations give rise to some new constraints on configurations of embedded spheres in 4-manifolds. Using similar methods, we also obtain new constraints on embeddings of real projective planes and spheres with a cusp singularity. Moreover, we show that the existence of certain configurations of surfaces would give rise to 4-manifolds of non-simple type. Our proof makes use of equivariant Seiberg–Witten invariants as well as a gluing formula for the relative Seiberg–Witten invariants of 4-manifolds with positive scalar curvature boundary.